As mentioned in the introduction, it is shown in [1]} that some Carleson measure estimate implies some quantitative mutual absolute continuity, namely, the \(A_\infty \)  condition, between the elliptic measure associated to an elliptic operator with real, \(L^\infty \)  coefficients and the Lebesgue measure. In [2]}, it is verified that this result also holds for elliptic operators having a \(\operatorname{BMO}\)  anti-symmetric part. To understand the precise statement and its connection to Theorem REF , we first need some notations and definitions.
